Cannot select individual bones of armature appeneded from 2.80 into 2.79
I think I found a workaround for this problem in case anyone else encounters it.

Create a new armature with a single bone in your project file (Shift + A Armature > Single Bone).

In Object mode, select your problematic armature (the one you can't select bones from in pose mode), Shift select your new single bone armature, and join the two (Ctrl + J ).

When I did this I was able to select all of my original bones in pose mode.